Rowan is just another name in the flowers/nature group: I know one from Nottingham. Northern perhaps, because of the spread of the tree, but not just Scottish.
The question said British names: Arthur is certainly about as British as you get but were UK names really meant? Anything ending -bert or -ric is going to be specifically English. (Robert the Bruce just shows how Anglicised the Scotish Lowlands were.) The Anglo-Saxon female names do seem to be unfashionable now, but I gather there was a spate of "Anglo-Saxon pride" in the 19th century, so perhaps we're just at the end of that rather than a rather longer chain.
Which are the original British names - can they be identified with current Welsh/Cornish/Breton names or have they changed too much with the times?